onday nalysis eminaraik/ma/2017/monanae.pdfonday nalysis eminar no. 1 (10 april 2017) 2 no. 2 (24...

Monday Analysis SeminarNo. 1 (10 April 2017) 2No. 2 (24 April 2017) 3No. 3 (22 May 2017) 4No. 4 (22 May 2017) 5No. 5 (5 June 2017) 6No. 6 (5 June 2017) 7No. 7 (3 July 2017) 8No. 8 (24 July 2017) 9No. 9 (31 July 2017) 10No. 10 (7 August 2017) 11No. 11 (7 August 2017) 12No. 12 (7 August 2017) 13No. 13 (2 October 2017) 14No. 14 (2 November 2017 (Thursday)) 15No. 15 (13 November 2017) 16No. 16 (30 November 2017 (Thursday)) 17No. 17 (1 December 2017 (Friday)) 18No. 18 (14 December 2017) 19第 19回 (2018年 1月 22日) 20No. 20 (24 January 2018 (Wednesday)) 21第 21回 (2018年 1月 29日) 22No. 22 (5 February 2018) 23No. 23 (5 March 2018) 24No. 24 (14 March 2018 (Wednesday)) 25No. 25 (27 March 2018 (Tuesday)) 26

Monday Analysis SeminarNo. 1 (2017 Academic Year)

Speaker: Hiroaki Aikawa (Hokkaido University)

Title: Dichotomy of global capacity density and the first eigenvalue of theLaplacian

Date: 10 April 2017 (:::::::::::::::15:00 – 16:30)

Place: Faculty of Science Building #3 Room 210

Abstract: Keywords: capacity density, first eigenvalue, Hardy’s inequality,inradius, capacitary width, Faraday cage principle, torsion function,survival probability.

Note.:::::::::::::::::::::::::::::::::::::::::::::::::::::Time changes for each lecture within 14:45–18:00.


Speaker: Takanobu Hara (Tokyo Metropolitan University)

Title: Interpolation properties of reverse Hölder inequalities and their ap-plications to Harnack inequalities

Date: 24 April 2017 (:::::::::::::::15:00 – 16:30)


Abstract: Key words: reverse Hölder inequality, Harnack inequality, nonlinearelliptic equations, p-Laplacian, metric space, doubling measure



Speaker: Shuichi Sato (Kanazawa University)

Title: Mapping properties of some square functions with Riesz potentials

Date: 22 May 2017 (:::::::::::::::15:00 – 16:00)


Note.:::::::::::::::::::::::::::::The first lecture on this day.


Speaker: Shuichi Sato (Kanazawa University)

Title: Functions of Marcinkiewicz type and Sobolev spaces

Date: 22 May 2017 (:::::::::::::::16:30 – 17:30)


Note.::::::::::::::::::::::::::::::::The second lecture on this day.


Speaker: Yusuke Isono (RIMS, Kyoto University)

Title: On fundamental groups of tensor product II1 factors

Date: 5 June 2017 (:::::::::::::::14:45 – 15:45)


Abstract: In the first half of the seminar, I give an introductory lecture onvon Nemann algebras for young students and non-specialists. Iparticularly focus on fundamental issues on von Neumann algebratheory.

In the second half, I talk about an invariant for von Neumannalgebras called fundamental groups. I introduce my recent workon this invariant which states a general behavior for tensor productalgebras. This is also for non-specialists.

Note.:::::::::::::::::::::::::::::::::::::::::Takeishi’s lecture follows after a break.


Speaker: Takuya Takeishi (RIMS, Kyoto University)

Title: On the classification problem of Bost-Connes systems

Date: 5 June 2017 (:::::::::::::::15:50 – 16:50)


Note.::::::::::::::::::::::::::::::::::This talk follows Isono’s lecture.


Speaker: Rikio Yondeda (Kanazawa University)

Title: Pointwise multiplier of the weighted Bergman spaces into the weightedBergman spaces

Date: 3 July 2017 (::::::::::::::15:00 – 16:30)


Abstract: We study the multiplication operators Mg on the weighted Bergmanspaces, the weighted Dirichlet spaces, the Hardy space. In partic-ular, pointwise multipliers from the weighted Bergman spaces tothe another weighted Bergman spaces are characterized by using theintegration operator Ig, Jg and the multiplication operators Mg.

Key Words and Phrases : integration operator, Bergman space,Hardy space, boundedness



Speaker: Marcel Schmidt (Mathematical Institute Friedrich-Schiller-Universität)

Title: Does diffusion determine the geometry?

Date: 24 July 2017 (:::::::::::::::15:00 – 16:30)


Abstract: Can one hear the shape of a drum? In mathematical terms thisfamous question of M. Kac asks whether two unitarily equivalentLaplacians live on the same geometric object. It is now known, thatthe answer to this question is negative in general.

Following an idea of Wolfgang Arendt, we replace the unitarytransformation intertwining the Laplacians by an order preservingone and then ask how much of the geometry is preserved. In thissituation the associated semigroups, which encode diffusion, areequivalent up to an order isomorphism. Therefore, the questionbecomes as stated in the title and we try to provide an answer ingreat generality. In particular, we discuss the situation for graphLaplacians and Laplacians on metric measure spaces. (this is jointwork with Matthias Keller, Daniel Lenz and Melchior Wirth)



Speaker: Tsubasa Itoh (Miyazaki University)

Title: The growth of the vorticity gradient for the two-dimensional Eulerflows on domains with cusps

Date: 31 July 2017 (:::::::::::::::15:00 – 16:30)




Speaker: Matti Vuorinen (University of Turku, Finland)

Title: Geometry of domains and maps

Date: 7 August 2017 (::::::::::::::13:30 – 15:00)


Abstract: My talk will deal with the study of geometric properties of domainsin Rn and quasiconformal maps defined on them. An important ideain this work is the study of how distances are changed under maps.The variation of geometric and topological properties of balls with afixed center and varying radius reflects the nature of the boundary ofthe domain. Metrics can be defined in many ways, e.g. in terms ofcapacity, angles or distances and each geometry has different balls.We also employ the number of Whitney cubes of a given generationfor this purpose. Mostly I will discuss results from my joint papersin arXiv during the past five years.

Note.:::::::::::::::::::::::::::::::::::::::::Reijonen’s lecture follows after a break.


Speaker: Atte Reijonen (University of Eastern Finland/東北大学大学院情報科学研究科)

Title: Derivatives of inner functions in weighted Bergman spaces

Date: 7 August 2017 (::::::::::::::15:30 – 16:30)


Abstract: For a Blaschke product B whose zeros lie in a Stolz domain, we finda condition regarding a weight w which guarantees that B’ belongsto the Bergman space induced by w. In addition, the sharpness ofthis condition is considered.

Note.::::::::::::::::::::::::::::::::::::::This talk follows Vuorinen’s lecture.


Speaker: Tomohiro Hayase (University of Tokyo)

Title: Random matrices and Bayesian statistics

Date: 7 August 2017 (::::::::::::::16:45 – 18:00)


Abstract: Sometimes random matrices appear in the analysis of statisticalmodels. Large random matrices have nice properties; their asymp-totic eigenvalue distributions are deterministic, and their traces areasymptotically normally distributed. We introduce some of theirapplications to (Bayesian) statistical estimations.

Note.:::::::::::::::::::::::::::::::The third lecture on August 7.


Speaker: Shuhei Kuwahara (Sapporo Seishu High School)

Title: Reducing subspaces for classes of Toeplitz operators over Hilbertspaces of analytic functions

Date: 2 October 2017 (::::::::::::::15:00 – 16:30)


Abstract: Keywords：reducing subspaces, weighted Hardy spaces, Bergmanspaces, bidisk, shift operators, multiplication operators, Toeplitzoperators, commutant, compact operators



Speaker: Yoshihiko Sano (Shizuoka University)

Title: 中空糸膜を介したガス溶解の数学モデルと人工心肺への応用

Date: 2 November 2017 (Thursday) (:::::::::::::::15:00 – 16:00)


Note.:::::::::::::::::::::::::::Different day of the week.


Speaker: Maya Zhelyazkova (Sofia University, Bulgaria)

Title: Spatial Thresholding Procedures for fMRI Analysis

Date: 13 November 2017 (::::::::::::::15:00 – 16:00)


Abstract: Many fMRI experiments have a common objective of identifyingactive voxels. This is commonly done in single subject experimentsfor example by performing individual voxelwise tests of the null hy-pothesis that the observed time course is not significantly related toan assigned reference function. A voxel activation map is then con-structed by applying a thresholding rule to the resulting t-statistics.Typically the task related activation is expected to occur in clustersrather than in isolated single voxels. A variety of spatial thresh-olding techniques have been proposed to reflect this belief includingsmoothing the raw t-statistics, cluster size inference, and spatial mix-ture modeling. We examined the performance of these proceduresfirst in terms of Receiver Operating Characteristics (ROC) curves,second we considered the accuracy of these spatial thresholding pro-cedures in estimation of the size of the activation region in termsof bias and variance. Also, we propose and study a Bayesian spa-tial mixture model for the spatial thresholding problem. We applythis method to a real fMRI study and compare its performance insimulations with other methods proposed for fMRI analysis.



Speaker: Yuzuru Inahama (Kyushu University)

Title: Introduction to Rough Path Theory

Date: 30 November 2017 (Thursday) (::::::::::::::16:30 – 18:00)


Abstract: In this talk I will explain what rough path theory is all about. This isbasically a survey talk for non-experts. Simply put, rough path theoryis something like "de-randomization of Itô’s stochastic differentialequations." Loosely speaking, we first extend the line integral forgeneralized paths, i.e., rough paths, by using K. T. Chen’s theoryon iterated integrals of paths as a guide, then we use it to makeItô’s SDEs deterministic. It can be viewed as a generalization ofcontrolled ODEs. With this theory by T. Lyons, which is in a sensean antitehsis to Itô’s theory, we can look at SDEs from a very differentangle. It was born approximately 15 years ago, but only a few peoplestudied it at first. In my view it was around 2010 when rough paththeory became very active. (Moreover, two years ago this theorybore two children, which solves very singular stochastic PDEs likeKPZ equation or 3-dim dynamic Φ4 model with ideas from roughpath theory. One of the two got a Fields medal, which makes thefuture of rough path look more bright.)



Speaker: Masato Hoshino (Waseda University)

Title: Global well-posedness of the stochastic complex Ginzburg-Landauequation

Date: 1 December 2017 (Friday) (:::::::::::::::14:45 – 16:00)


Abstract: We discuss the solvability of the complex Ginzburg-Landau equationwith a space-time Gaussian white noise, on the 3-dimensional torus.Since this equation has a singular term, its solution is defined afterperforming a suitable renormalization. This part is a stochasticproblem. The local well-posedness was shown by Hoshino, Inahamaand Naganuma. We furthermore show the global well-posedness byusing a priori L3+ inequality. This part is a purely PDE problem.

Note.::::::::::::::::::::::::::::::::::::::Different place and day of the week.


Speaker: Wojciech Młotkowski (Wrocław University, Poland)

Title: Cauchy-Stieltjes families with polynomial variance functions

Date: 14 December 2017 (:::::::::::::::16:30 – 18:00)


Abstract: We study variance functions of the Cauchy-Stielties kernel (CSK)families generated by compactly supported centered probabilitymeasures. We describe several operations that allow to constructadditional variance functions from known ones. We also construct aclass of examples which we believe exhausts all cubic variance func-tions, and provide other examples of polynomial variance functions.(Joint work with Wlodzimierz Bryc (University of Cincinnati) andRaouf Fakhfakh (Sfax University, Tunisia))


月曜解析セミナーMonday Analysis Seminar

第19回 (平成29年度)No. 19 (2017 Academic Year)

日時: 2018年 1月 22日 (::::::::::::::14:40 – 18:00)

Date: 22 January 2018 (::::::::::::::14:40 – 18:00)

場所: 北海道大学理学部 3号館 210Place: Faculty of Science Buliding #3 Room 210

講演者: 高橋直暉題目: 無限次元系における quantum relative entropyの性質

講演者: 清水裕也題目: 無限次元ユニタリ群の球関数とシューア関数について

講演者: 中澤麗花題目: GUEにおける固有値の分布の漸近解析について

講演者: 池田知寛題目: Mixing Time of the random walk on the n-cycle and Cutoff of

hypercube

講演者: 米山昇平題目: 離散群と関数解析

講演者: 松尾有平題目: 複素力学系に関わる C∗環とそのKMS state

講演者: 吉田啓佑題目: Kirchberg’s tensor product theorem

注意:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::修士論文発表会です．本番通り 15分講演，5分質疑で行います．


Speaker: Takaaki Nara (University of Tokyo)

Title: Application of potential theory and complex analysis to biomag-netic inverse problems: identification of neural current sources andelectrical properties inside the human brain

Date: 24 January 2018 (Wednesday) (16:30 – 18:00)

Place: Faculty of Science Building::::::::::::::#4 Room 501

Abstract: Key words: inverse problems, Stokes theorem, Dbar equation,epilepsy, conductivity, permittivity

Note.::::::::::::::::::::::::::::::::::::::Different place and day of the week.

月曜解析セミナーMonday Analysis Seminar

第21回 (平成29年度)No. 21 (2017 Academic Year)

日時: 2018年 1月 29日 (::::::::::::::15:00 – 15:40)

Date: 29 January 2018 (::::::::::::::15:00 – 15:40)

場所: 北海道大学理学部 3号館 210Place: Faculty of Science Buliding #3 Room 210

講演者: 森下順貴題目: 有限自由確率論

講演者: 木村圭吾題目: 中心極限定理の精密化について

注意:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::修士論文発表会です．本番通り 15分講演，5分質疑で行います．


Speaker: Anatoly Golberg (Holon Institute of Technology, Israel)

Title: Homeomorphisms with integrally restricted p-moduli

Date: 5 February 2018 (::::::::::::::15:00 – 16:30)


Abstract: We consider classes of homeomorphisms of domains in Rn withintegrally bounded from above or below p-moduli of the familiesof curves and surfaces. Such mappings essentially extend the well-known customarily investigated classes of mappings such as qua-siconformal, quaiisometric, Lipschitzian, etc. In contrast to theseknown classes, our generalized classes can be defined without anyanalytic restrictions. However, various differential properties ofmappings can be derived on the base of estimates for p-moduli(p-capacities of condensers).

In the talk we survey the known results in this field, regardingmainly the regularity features of such mappings. A collection ofopen related problems will be also presented.


Speaker: Massimo Lanza De Cristoforis (University of Padova)

Title: A functional analytic approach to singular perturbation problems

Date: 5 March 2018 (:::::::::::::::15:00 – 16:30)


Abstract: This talk is dedicated to the analysis of boundary value problems onsingularly perturbed domains by an approach which is alternative tothose of asymptotic analysis and of homogenization theory, and hasthe character of a general presentation.

In particular, we will consider a certain linear or nonlinear ellipticboundary value problem on a domain with one or possibly infinitelymany holes, whose size is determined by a positive parameter ϵand we will consider a family of solutions depending on ϵ as ϵapproaches 0. Then we shall represent the dependence on ϵ of thefamily of solutions, or of corresponding functionals of the solutionssuch as the energy integral, in terms of possibly singular at 0 butknown functions of ϵ such as ϵ−1 or log ϵ , and in terms of possiblyunknown real analytic maps.

Boundary value problems on singularly perturbed domains ap-pear in the applications such as those of the analysis of compositematerials.


Speaker: Hayato Saigo (Nagahama Institute of Bio-Science and Technology)

Title: The ABC of Category Theory and Infinite Analysis

Date: 14 March 2018 (Wednesday) (::::::::::::::::16:30 — 18:00)




Speaker: Jun Kigami (Kyoto University)

Title: Weighted partition of a compact metrizable space, its hyperbolicityand Ahlfors regular conformal dimension

Date: 27 March 2018 (Tuesday) (:::::::::::::::15:00 – 16:30)


Abstract: Successive divisions of compact metric spaces appear in many dif-ferent areas of mathematics such as the construction of self-similarsets, Markov partition associated with hyperbolic dynamical sys-tems, dyadic cubes associated with a doubling metric space. Thecommon feature in these is to divide a space into a finite number ofsubsets, then divide each subset into pieces and repeat this processagain and again. In this paper we generalize such successive divisonsand call them partitions. Given a partition, we consider the notionof a weight function assigning a “size” to each piece of the partition.Intuitively we believe that a partition and a weight function shouldprovide a “geometry” and an “analysis” on the space of our interest.In this paper, we are going to pursue this idea in three parts. Inthe first part, the metrizability of a weight function is shown to beequivalent to the Gromov hyperbolicity of the graph associated withthe weight function. In the second part, the notions like bi-Lipschitzequivalence, Ahlfors regularity, the volume doubling property andquasisymmetry will be shown to be equivalent to certain propertiesof weight functions. In particular, we find that quasisymmetry andthe volume doubling property are the same notion in the world ofweight functions. In the third part, a characterization of the Ahlforsregular conformal dimension of a compact metric space is given asthe critical index p of p-energies associated with the partition andthe weight function corresponding to the metric.


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